The symbols of the Chinese zodiac are rather complex. When most people think about the Chinese zodiac, they think about the 12 zodiac animals which are known as the Earthly Branches. However, the symbols in the Chinese zodiac also interact with the five elements, called the Heavenly Stems, generating a 60 year cycle which encompasses all 12 animals and each animal's possible five elemental associations. In Chinese astrology, knowing your Earthly Branch is only one part of the equation.
When calculating where your birthday falls within the Chinese zodiac, it is important to remember that the Chinese zodiac runs on a lunar calendar, not the Roman calendar. Therefore, the zodiac symbols change at the lunar new year, rather than on the first of January. As a result, someone born in a year such as 1970 could be a rooster or a dog, depending on his or her date of birth.
In order, the Earthly Branches are: rat, ox, tiger, rabbit, dragon, snake, horse, sheep, monkey, rooster, dog and boar. Each of these symbols in the Chinese zodiac is associated with specific traits, including things like loyalty, generosity, impatience, kindness, eccentricity, and intelligence, among many others. In addition, someone's character is further determined by which of the Heavenly Stems influences his or her zodiac symbol. The Heavenly Stems are metal, water, wood, fire, and earth, and they can further be broken into yin and yang, with odd years being yin, while even years are yang.
In Chinese astrology, other factors are taken into account when profiling someone as well, including the date and time of birth, and the location at which someone is born. Considering all of the possible permutations can get quite involved and complex, and people who want astrological profiles which conform with the rules of the Chinese zodiac generally go to professionals to ensure that everything is considered.
If you want to find your Chinese zodiac symbol, numerous websites have charts of the Earthly Branches linked to their associated dates of birth in the Roman calendar. It is also possible to find more involved charts which include information about the Heavenly Stems, if you want more precise details about your Chinese zodiac symbol.